We consider the forward Kolmogorov equation that corresponds to a generalized version of the BPDL model. In its classical form, the Bolker-Pacala model is a purely spatially-structured microscopic model for a population of plants involving the birth, dispersal, and either natural death or death by competition for resources and can be modeled as a jump process in the space of positive measures over \(\mathbb {R}^d\) . However, in certain models of adaptive evolution it is the mutation of traits that play a role, instead of spatial evolution (see [1]}, [2]}, [3]}). Moreover, if one wants to model multiple interacting species or marked configuration spaces, more general spaces than \(\mathbb {R}^d\)  are needed [4]}, [5]}).
